Vertex algebras and algebraic curves

Asterisque

Volumn , Issue 276, 2002, Pages 299-339

  Frenkel, Edward ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3242717110     PISSN: 03031179     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Article

References (70)

1. [ADKP] E. ARBARELLO, C. DE CONCINI, V. KAC and C. PROCESI - Moduli spaces of curves and representation theory, Comm. Math. Phys. 117 (1988) 1-36.
2. [BL] A. BEAUVILLE and Y. LASZLO - Conformal blocks and generalized theta functions, Comm. Math. Phys. 164 (1994) 385-419.
3. [BB] A. BEILINSON and J. BERNSTEIN - A Proof of Jantzen Conjectures, Advances in Soviet Mathematics 10, Part 1, pp. 1-50, AMS 1993.
4. [BD1] A. BEILINSON and V. DRINFELD - Affine Kac-Moody algebras and poly-differentials, Int. Math. Res. Notices 1 (1994) 1-11.
5. [BD2] A. BEILINSON and V. DRINFELD - Quantization of Hitchin's Integrable System and Hecke eigensheaves. Preprint.
6. [BD3] A. BEILINSON and V. DRINFELD - Chiral Algebras. Preprint.
7. [BFM] A. BEILINSON, B. FEIGIN and B. MAZUR - Introduction to Algebraic Field Theory on Curves. Preprint.
8. [BG] A. BEILINSON and V. GINZBURG - Infinitesimal structure of moduli spaces of G-bundles, Duke Math. J. IMRN 4 (1992) 63-74.
9. [BS] A. BEILINSON and V. SCHECHTMAN - Determinant bundles and Virasoro algebras, Comm. Math. Phys. 118 (1988) 051-701.
10. [BPZ] A. BELAVIN, A. POLYAKOV and A. ZAMOLODCHIIKOV - Infinite conformai symmetries in two-dimensional quantum field theory, Nucl. Phys. B241 (1984) 333-380.
11. [BF] D. BEN-ZVI and E. FRENKEL - Vertex algebras and algebraic curves, book in preparation.
12. [B1] R. BORCHERDS - Vertex algebras, Kac-Moody algebras and the monster, Proc. Nat. Acad. Sci. USA 83 (1986) 3068-3071.
13. [B2] R. BORCHERDS - Monstrous moonshine and monstrous Lie superalgebras, Invent. Math. 109 (1992) 405-444.
14. [B3] R. BORCHERDS - Quantum vertex algebras, Preprint math.QA/9903038.
15. [Bo1] L. BORISOV - Introduction to the vertex algebra approach to mirror symmetry, Preprint math.AG/9912195.
16. [BoL] L. BORISOV and A. LIBGOBER - Elliptic genera of toric varieties and applications to mirror symmetry, Invent. Math. 140 (2000) 453-485.
17. [dBT] J. de BOER and T. TJIN - The relation between quantum W-algebras and Lie algebras, Comm. Math. Phys. 160 (1994) 317-332.
18. [dFMS] P. di FRANCESCO, P. MATHIEU and D. SENECHAL - Conformal Field Theory. Springer-Verlag 1997.
19. [D1] C. DONC - Vertex algebras associated with even lattices, J. Algebra 161 (1993) 245-265.
20. [D2] C. DONG - Representations of the moonshine module vertex operator algebra, Contemp. Math. 175 (1994) 27-36.
21. [DLM] C. DONG, H. Li and G. MASON - Twisted representations of vertex operator algebras, Math. Ann. 310 (1998) 571-600.
22. [DS] V. DRINFELD and V. SOKOLOV - Lie algebras and KdV type equations, J. Sov. Math. 30 (1985) 1975-2036.
23. [EK] P. ETINGOF and D. KAZHDAN - Quantization of Lie bialgebras. V, Preprint math.QA/9808121.
24. [Fa] G. FALTINGS - A proof of the Verlinde formula, J. Alg. Gcom. 3 (1994) 347-374.
25. n symmetry, Int. J. Mod. Phys. A3 (1988), 507-520.
26. [Fe1] B. FEIGIN - The semi-infinite cohomology of Kac-Moody and Virasoro Lie algebras, Russ. Math. Surv. 39, No. 2 (1984) 155-156.
27. [FF1] B. FEIGIN and E. FRENKEL - A family of representations of affine Lie algebras, Russ. Math. Surv. 43, No. 5 (1988) 221-222.
28. [FF2] B. FEIGIN and E. FRENKEL - Affine Kac-Moody algebras and semi-infinite flag manifolds, Comm. Math. Phys. 128 (1990) 161-189.
29. [FF3] B. FEIGIN and E. FRENKEL - Affine Kac-Moody algebras at the critical level and Gelfand-Dikii algebras, Int. Jour. Mod. Phys. A7, Suppl. 1A (1992) 197-215.
30. [FF4] B. FEIGIN and E. FRENKEL - Integrals of Motion and Quantum Groups, in Lect. Notes in Math. 1620, pp. 349-418, Springer-Verlag 1996.
31. [FS] B. FEIGIN and A. STOYANOVSKY - Realization of a modular functor in the space of differentials, and geometric approximation of the moduli space of G-bundles, Funct. Anal. Appl. 28 (1994) 257-275.
32. [FKW] E. FRENKEL, V. KAC and M. WAKIMOTO - Characters and fusion rules for W-algebras via quantized Drinfeld-Sokolov reduction, Comm. Math. Phys. 147 (1992), 295-328.
33. N with central charge N, Comm. Math. Phys. 170 (1995) 337-357.
34. [FR] E. FRENKEL and N. RESHETIKHIN - Towards deformed chiral algebras, Preprint q-alg/9706023.
35. [FK] I. FRENKEL and V. KAC - Basic representations of affine Lie algebras and dual resonance models, Invent. Math. 62 (1980) 23-66.
36. [FGZ] I. FRENKEL, H. GARLAND and G. ZUCKERMAN - Semi-infinite cohomology and string theory, Proc. Nat. Acad. Sci. U.S.A. 83 (1986) 8442-8446.
37. [FLM] I. FRENKEL, J. LEPOWSKY and A. MEURMAN - Vertex Operator Algebras and the Monster. Academic Press 1988.
38. [FHL] I. FRENKEL, Y.-Z. HUANG and J. LEPOWSKY - On axiomatic approaches to vertex operator algebras and modules. Mem. Amer. Math. Soc, 104 (1993), no. 494.
39. [FZ] I. FRENKEL and Y. ZHU - Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Math. J. 60 (1992) 123-168.
40. [FrS] D. FRIEDAN and S. SHENKER - The analytic geometry of two-dimensional conformai field theory, Nucl. Phys. B281 (1987) 509-545.
41. [G] D. GAITSGORY - Notes on 2D Conformal Field Theory and String Theory, in Quantum fields and strings: a course for mathematicians, Vol. 2, pp. 1017-1089, AMS 1999.
42. [Ga] K. GAWEDZKI - Conformai field theory, Sém. Bourbaki, Exp. 704, Astérisque 177-178 (1989) 95-126.
43. [GKF] I.M. GELFAND, D. A. KAZHDAN and D.B. FUCHS - The actions of infinite-dimensional Lie algebras, Funct. Anal. Appl. 6 (1972) 9-13.
44. [Gi] V. GINZBURG - Resolution of diagonals and moduli spaces, in The moduli space of curves, Progress in Math. 120, pp. 231-266, Birkhäuser 1995.
45. [Go] P. GODDAHD - Meromorphic conformal field theory, in Infinite-dimensional Lie algebras and groups, V. Kac (ed.), pp. 556-587, World Scientific 1989.
46. [GKO] P. GODDARD, A. KENT and D. OLIVE - Unitary representations of the Virasoro and super-Virasoro algebras, Comm. Math. Phys. 103 (1986) 105-119.
47. [CMS] V. GORBOUNOV, F. MALIKOV and V. SCHECHTMAN - Gerbes of chiral differential operators. I, math.AG/9906116; II, math.AG/0003170.
48. [Gu] R. GUNNING - Lectures on Riemann Surfaces. Princeton University Press 1966.
49. [Hu] Y.-Z. HUANG - Two-dimensional conformal geometry and vertex operator algebras. Progress in Math. 148. Birkhäuser 1997.
50. [HL] Y.-Z. HUANG and J. LEPOWSKY - On the "D-module and formal variable approaches to vertex algebras, in Topics in geometry, pp. 175-202, Birkhäuser 1996.
51. [K1] V. KAC - Infinite-dimensional Lie algebras, Third Edition. Cambridge University Press 1990.
52. [K2] V. KAC - Vertex Algebras for Beginners, Second Edition. AMS 1998.
53. [K3] V. KAC - Formal distribution algebras and conformal algebras, in Proc. XXIIth ICMP, Brisbane, 1994, pp. 80-96, International Press 1999.
54. [KL] D. KAZHDAN and G. LUSZTIG - Tensor structures arising from affine Lie algebras IV, J. of AMS 7 (1993) 383-453.
55. [Ko] M. KONTSEVICH - The Virasoro algebra and Teichmüller spaces, Funct. Anal. Appl. 21 (1987), no. 2, 156-157.
56. [KNR] S. KUMAR, M.S. NARASIMHAN and A. RAMANATHAN - Infinite Grassmannians and moduli spaces of G-bundles, Math. Ann. 300 (1993) 395-423.
57. (1), Comm. Math. Phys. 62 (1978) 43-53.
58. H. Li - Local systems of vertex operators, vertex superalgebras and modules, J. Pure Appl. Alg. 109 (1996) 143-195.
59. [LZ] B. LIAN and G. ZUCKERMAN - Neu; perspectives on the BRST-algebraic structure of string theory, Comm. Math. Phys. 154 (1993) 613-646.
60. [MSV] A. MALIKOV, V. SCHECHTMAN and A. VAINTROB - Chiral deRham complex, Comm. Math. Phys. 204 (1999) 439-473.
61. [SV2] V. SCHECHTMAN and A. VARCHENKO - Quantum groups and homology of local systems, in Algebraic Geometry and Analytic Geometry, M. Kashiwara and T. Miwa (eds.), pp. 182-191, Springer-Verlag 1991.
62. [Se] G. SEGAL - The Definition of Conformal Field Theory, unpublished manuscript.
63. [So] C. SORGER - La formule de Verlinde, Sém. Bourbaki, Exp. 793, Astérisque 237 (1996) 87-114.
64. 1 and monodromy representations of the braid group, in Adv. Stud. Pure Math 16, pp. 297-372, Academic Press 1988.
65. [TUY] A. TSUCHIYA, K. UENO and Y. YAMADA - Conformal field theory on universal family of stable curves with gauge symmetries, Adv. Stud. Pure Math. 19, pp. 459-566, Academic Press 1989.
66. (1) Comm. Math. Phys. 104 (1986) 605-609.
67. [Wa] W. WANG - Rationality of Virasoro vertex operator algebras, Duke Math. J. IMRN 7 (1993) 197-211.
68. [Wi] E. WITTEN - Quantum field theory, Grassmannians and algebraic curves, Comm. Math. Phys 113 (1988) 529-600.
69. [Z1] Y. ZHU - Modular invariance of characters of vertex operator algebras, J. AMS 9 (1996) 237-302.
70. [Z2] Y. ZHU - Global vertex operators on Riemann surfaces, Comm. Math. Phys. 165 (1994) 485-531.